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UESTI What is the value of c in the interval (16, 36) guaranteed by the Mean Value Theorem for the function s(x) = 6√x-6? Give your answer as an exact fraction or radical if necessary. Do not include "c=" in your answer. Provide your answer below: Content attribution - Previous W S #3 20 F3 X E D command I $ 4 838 FA R C % 5 F MacBook Air T V (0) 6 . G Y & 7 B 47 H ★ U 8 FO J N ( 9 D K M 1 O - V 1 FEEDBACK C P 43:02 10/20 i 10 1 1 delete

UESTI What is the value of c in the interval (16, 36) guaranteed by the Mean Value Theorem for the function s(x) = 6√x-6? Give your answer as an exact fraction or radical if necessary. Do not include "c=" in your answer. Provide your answer below: Content attribution - Previous W S #3 20 F3 X E D command I $ 4 838 FA R C % 5 F MacBook Air T V (0) 6 . G Y & 7 B 47 H ★ U 8 FO J N ( 9 D K M 1 O - V 1 FEEDBACK C P 43:02 10/20 i 10 1 1 delete

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Educational Website Content:** **Calculus Problem: Mean Value Theorem** --- **Problem Statement:** What is the value of \( c \) in the interval \((16, 36)\) guaranteed by the Mean Value Theorem for the function \( s(x) = 6\sqrt{x} - 6? \) Give your answer as an exact fraction or radical if necessary. Do not include “c =” in your answer. --- **Answer Box:** Provide your answer below: ``` ______________________________________________________ ``` *(There is a cursor indicating where to type the answer)* --- **Additional Resources:** - **Previous** - [Feedback](#) - Content Attribution --- **Explanation:** *This problem requires the application of the Mean Value Theorem (MVT) which states that for a function \( f \) continuous on \([a, b]\) and differentiable on \((a, b)\), there exists a point \( c \) in \((a, b)\) such that \( f'(c) = \frac{f(b) - f(a)}{b - a} \).* To summarize, in this calculus problem, we must: 1. Find the derivative of the function \( s(x) = 6\sqrt{x} - 6 \). 2. Apply the Mean Value Theorem to find the exact \( c \) in the interval \((16, 36)\). Happy Learning!
Transcribed Image Text:**Educational Website Content:** **Calculus Problem: Mean Value Theorem** --- **Problem Statement:** What is the value of \( c \) in the interval \((16, 36)\) guaranteed by the Mean Value Theorem for the function \( s(x) = 6\sqrt{x} - 6? \) Give your answer as an exact fraction or radical if necessary. Do not include “c =” in your answer. --- **Answer Box:** Provide your answer below: ``` ______________________________________________________ ``` *(There is a cursor indicating where to type the answer)* --- **Additional Resources:** - **Previous** - [Feedback](#) - Content Attribution --- **Explanation:** *This problem requires the application of the Mean Value Theorem (MVT) which states that for a function \( f \) continuous on \([a, b]\) and differentiable on \((a, b)\), there exists a point \( c \) in \((a, b)\) such that \( f'(c) = \frac{f(b) - f(a)}{b - a} \).* To summarize, in this calculus problem, we must: 1. Find the derivative of the function \( s(x) = 6\sqrt{x} - 6 \). 2. Apply the Mean Value Theorem to find the exact \( c \) in the interval \((16, 36)\). Happy Learning!
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